In Hyland et al. (1980), Hyland, Johnstone and Pitts introduced the notion of tripos for the purpose of organizing the construction of realizability toposes in a way that generalizes the construction of localic toposes from complete Heyting algebras. In Pitts (2002), one finds a generalization of this notion eliminating an unnecessary assumption of Hyland et al. (1980). The aim of this paper is to characterize triposes over a base topos ${\cal S}$ in terms of so-called constant objects functors from ${\cal S}$ to some elementary topos. Our characterization is slightly different from the one in Pitts’s PhD Thesis (Pitts, 1981) and motivated by the fibered view of geometric morphisms as described in Streicher (2020). In particular, we discuss the question whether triposes over Set giving rise to equivalent toposes are already equivalent as triposes.

在海兰等人。(1980)，Hyland、Johnstone 和 Pitts 引入了tripos的概念，目的是组织可实现性拓扑的构造，以一种从完整的 Heyting 代数推广局部拓扑构造的方式。在 Pitts (2002) 中，人们发现了这一概念的推广，消除了 Hyland 等人的不必要假设。（1980 年）。本文的目的是根据来自${\cal S}$的所谓常量对象函子来表征基本拓扑${\cal S}$上的三元组到一些基本的拓扑。我们的描述与 Pitts 的博士论文（Pitts，1981）中的描述略有不同，并且受到 Streicher（2020）中描述的几何态射的纤维化观点的推动。特别是，我们讨论了一个问题，即产生等价拓扑的Set上的三元组是否已经与三元组等价。